All Questions
Tagged with equivariant ag.algebraic-geometry
9 questions with no upvoted or accepted answers
7
votes
0
answers
258
views
Ample divisors on $T$-varieties
Question: how does one use a torus action to help decide whether a divisor or line bundle is ample?
In more detail: I have a (normal, but usually rather singular) $T$-variety $X$, where $T$ is an ...
- 6,162
5
votes
0
answers
334
views
T-Equivariant trivialization of a principal G-bundle
Let $k$ be a field, let $G$ be an algebraic group scheme over $k$ and let $T = \textrm{Spec } k[x, x^{-1}]$ be a one-dimensional torus. Does there exist
a scheme $X$ over $k$,
an algebraic $T$-action ...
- 562
4
votes
0
answers
155
views
$\pm 1$-equivariant perverse sheaves on the affine line
Let $G=\mathbb{Z}/\mathbb{2Z}$ act by the map $z\mapsto -z$ on a complex line $\mathbb{C}$. The category $\mathcal{Perv}(\mathbb{C})$ of perverse sheaves smooth along the stratification by the origin ...
- 1,071
4
votes
0
answers
402
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Equivariant sheaves and simplicial varieties
I would like to proof the following theorem:
Let $\pi:X\rightarrow X/G$ be a principal $G$-bundle (say of varieties, Zariski locally trivial), then $\pi^*$ induces an equivalence between modules on ...
- 13.2k
3
votes
0
answers
662
views
Equivariant Riemann-Roch on DM stacks?
Does an equivariant version of (Toen)-Riemann-Roch theorem hold say over a smooth Deligne-Mumford stack $X$ over the complex numbers?
Any references that state this explicitely?
Are there formulas ...
- 23.4k
3
votes
0
answers
443
views
Equivariant form of Nagata's compactification theorem?
Given a finite group $G$ acting on an algebraic variety $X$ (let's say over $\mathbb C$, if that helps), is there always a proper variety $\bar X$ with a $G$ action such that $X \to \bar X$ is a $G$-...
- 3,017
3
votes
0
answers
160
views
Monodromy along strata of a pushforward
Work with complex varieties and constructible sheaves on the complex analytic site. All functors will be tacitly derived.
Let $X$ be a variety acted upon by a connected linear algebraic group. Let $X ...
- 1,595
1
vote
0
answers
81
views
Is every homogeneous line bundle pulled back from the quotient stack?
Let $G= \mathbb{G}_m^k$ act on a variety $X$.
Let $\mathcal{L}$ be a line bundle on $X$ and assume that for each $g \in G$ the pullback $g^\star \mathcal{L}$ is isomorphic to $\mathcal{L}$.
Does it ...
- 323
1
vote
0
answers
94
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Invariant category and coinvariant category under group action
Let $\mathcal{C}$ be a category with a finite group action $G$, There is a notion called G-equivariant category, denoted by $\mathcal{C}^G$. In the paper Kuznetsov's Fano threefold conjecture via K3 ...
- 1,982